Specularity map vs Fresnel
In an ideal situation you would use both actually.
The Fresnel node will simulate the real physical property of many surfaces that causes more light reflection grazing angles. Think looking through a glass pane perpendicularly (transparent, see through) or sideways (you will see more reflection).

The specular map will deal with differences of reflectivity along the surface of the material due to uneven or varying surface properties (more polished areas versus more rough surfaces)

To achieve to most realistic results your could mix both with a Color Mix node and tweat blending values to the desired result

Edit: Here are two examples, either add the texture to the roughness input of a glossy shader



Or add the image texture to the mix value of a shader mix node.



Or both, and if desired you can additionally use it for bump mapping if necessary